| A) He ate, however; he didn't sleep. | B) He ate however, he; didn't sleep. | 
| C) He ate; however, he didn't sleep. | D) None of the above | 
Explanation:
Like commas, semicolons indicate an audible pause — slightly longer than a comma's, but short of a period's full stop.
Rules for Semicolon ::
1. A semicolon can replace a period if the writer wishes to narrow the gap between two closely linked sentences.
2. Use a semicolon before such words and terms as namely, however, therefore, that is, i.e., for example, e.g., for instance, etc., when they introduce a complete sentence. It is also preferable to use a comma after these words and terms.
3. Avoid a semicolon when a dependent clause comes before an independent clause.
4. Use a semicolon to separate units of a series when one or more of the units contain commas.
Hence according to rule no. 2) option (C) He ate; however, he didn't sleep is correctly puctuated with a semicolon.
 
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